Abstract

The continuous shrinkage of minimum feature size in integrated circuit (IC) fabrication incurs more and more serious distortion in the optical projection lithography process, generating circuit patterns that deviate significantly from the desired ones. Conventional resolution enhancement techniques (RETs) are facing critical challenges in compensating such increasingly severe distortion. In this paper, we adopt the approach of inverse lithography in the mask design, which is a branch of design methodology to treat it as an inverse mathematical problem. We focus on using pixel-based algorithms to design alternating phase-shifting masks with minimally distorted output, with the goal that the patterns generated should have high contrast and low dose sensitivity. This is achieved with a dynamic-programming-based initialization scheme to pre-assign phases to the layout when alternating phase-shifting masks are used. Pattern fidelity and worst case slopes are shown to improve with this initialization scheme, which are important for robustness considerations.

© 2008 Optical Society of America

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References

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  1. J. Plummer, M. Deal, and P. Griffin, Silicon VLSI Technology ??? Fundamentals, Practice and Modeling (Prentice Hall, 2000).
  2. C. A. Mack, "30 years of lithography simulation," Proc. SPIE 5754, 1-12 (2004).
    [CrossRef]
  3. F. Schellenberg, "Resolution enhancement technology: The past, the present, and extensions for the future," Proc. SPIE 5377, 1-20 (2004).
    [CrossRef]
  4. A. K.-K. Wong, Resolution enhancement techniques in optical lithography (SPIE Press, Bellingham, Washington, 2001).
    [CrossRef]
  5. K. Nashold and B. Saleh, "Image construction through diffraction-limited high-contrast imaging systems: An iterative approach," J. Opt. Soc. Am. A 2, 635-643 (1985).
    [CrossRef]
  6. B. Saleh and S. Sayegh, "Reductions of errors of microphotographic reproductions by optical corrections of original masks," Opt. Eng. 20, 781-784 (1981).
  7. S. Sherif, B. Saleh, and R. Leone, "Binary image synthesis using mixed linear integer programming," IEEE Trans. Image Process. 4, 1252-1257 (1995).
    [CrossRef] [PubMed]
  8. Y. Liu and A. Zakhor, "Binary and phase-shifting image design for optical lithography," IEEE Trans. Semicond. Manuf. 5, 138-151 (1992).
    [CrossRef]
  9. Y. Liu and A. Zakhor, "Optimal binary image design for optical lithography," Proc. SPIE 1264, 410-412 (1990).
  10. N. Cobb and A. Zakhor, "Fast sparse aerial image calculation for OPC," Proc. SPIE 2621, 534-545 (1995).
    [CrossRef]
  11. Y. C. Pati and T. Kailath, "Phase-shifting masks for microlithography automated design and mask requirements," J. Opt. Soc. Am. A 11, 2438-2452 (1994).
    [CrossRef]
  12. D. S. Abrams and L. Pang, "Fast inverse lithography technology," Proc. SPIE 6154, 534-542 (2006).
  13. C. Hung, B. Zhang, E. Guo, L. Pang, Y. Liu, K. Wang, and G. Dai, "Pushing the lithography limit: Applying inverse lithography technology (ILT) at the 65nm generation," Proc. SPIE 6154, 61541M (2006).
    [CrossRef]
  14. L. Pang, Y. Liu, and D. Abrams, "Inverse lithography technology (ILT): What is the impact to the photomask industry?" Proc. SPIE 6283, 62830X (2006).
    [CrossRef]
  15. A. Poonawala and P. Milanfar, "Prewarping techniques in imaging: Applications in nanotechnology and biotechnology," Proc. SPIE 5674, 114-127 (2005).
    [CrossRef]
  16. A. Poonawala and P. Milanfar, "OPC and PSM design using inverse lithography: A nonlinear optimization approach," Proc. SPIE 6154, 61543H (2006).
    [CrossRef]
  17. S. H. Chan, A. K. Wong, and E. Y. Lam, "Inverse synthesis of phase-shifting mask for optical lithography," in "OSA Topical Meeting in Signal Recovery and Synthesis," (2007), p. SMD3.
  18. X. Ma and G. R. Arce, "Generalized inverse lithography methods for phase-shifting mask design," Opt. Express 15, 15066-15079 (2007).
    [CrossRef] [PubMed]
  19. J. W. Goodman, Statistical Optics (Wiley-Interscience, 1985).
  20. J. W. Goodman, Introduction to Fourier Optics (Roberts and Company Publisher, Englewood, Colo, 2005), 3rd ed.
  21. Y. Granik, "Solving inverse problems of optimal microlithography," Proc. SPIE 5754, 506-526 (2004).
    [CrossRef]
  22. A. Poonawala and P. Milanfar, "Mask design for optical microlithography ???an inverse imaging problem," IEEE Trans. Image Process. 16, 774-788 (2007).
    [CrossRef] [PubMed]
  23. S. H. Chan and E. Y. Lam, "Inverse image problem of designing phase shifting masks in optical lithography," in "IEEE International Conference on Image Processing," (2008).
  24. P. E. Gill, W. Murray, and M. H. Wright, Practical optimization (Academic Press, London, 1986).
  25. W. Rudin, Principles of Mathematical Analysis (McGraw-Hill, 1976).
  26. M. Minoux, Mathematical programming theory and algorithms (John Wiley and Sons, Chichester, 1986).
  27. P. Berman, A. Kahng, D. Vidhani, H. Wang, and A. Zelikovsky, "Optimal phase conflict removal for layout of dark field alternating phase shifting masks," IEEE Trans.Comput.-Aided Des. 19, 175-187 (2000).
    [CrossRef]
  28. A. Moniwa and T. Terasawa, "Heuristic method for phase-conflict minimization in automatic phase-shift mask design," Jpn. J. Appl. Phys. 34, 6584-6589 (1995).
    [CrossRef]
  29. L. G. Shapiro and G. C. Stockman, Computer Vision (Prentice Hall, 2001).
  30. D. Halliday, R. Resnick, and K. S. Krane, Physics, (John Wiley and Sons, New York, 2002), 2nd ed., Vol. 2.

2007 (2)

A. Poonawala and P. Milanfar, "Mask design for optical microlithography ???an inverse imaging problem," IEEE Trans. Image Process. 16, 774-788 (2007).
[CrossRef] [PubMed]

X. Ma and G. R. Arce, "Generalized inverse lithography methods for phase-shifting mask design," Opt. Express 15, 15066-15079 (2007).
[CrossRef] [PubMed]

2006 (4)

A. Poonawala and P. Milanfar, "OPC and PSM design using inverse lithography: A nonlinear optimization approach," Proc. SPIE 6154, 61543H (2006).
[CrossRef]

D. S. Abrams and L. Pang, "Fast inverse lithography technology," Proc. SPIE 6154, 534-542 (2006).

C. Hung, B. Zhang, E. Guo, L. Pang, Y. Liu, K. Wang, and G. Dai, "Pushing the lithography limit: Applying inverse lithography technology (ILT) at the 65nm generation," Proc. SPIE 6154, 61541M (2006).
[CrossRef]

L. Pang, Y. Liu, and D. Abrams, "Inverse lithography technology (ILT): What is the impact to the photomask industry?" Proc. SPIE 6283, 62830X (2006).
[CrossRef]

2005 (1)

A. Poonawala and P. Milanfar, "Prewarping techniques in imaging: Applications in nanotechnology and biotechnology," Proc. SPIE 5674, 114-127 (2005).
[CrossRef]

2004 (3)

Y. Granik, "Solving inverse problems of optimal microlithography," Proc. SPIE 5754, 506-526 (2004).
[CrossRef]

C. A. Mack, "30 years of lithography simulation," Proc. SPIE 5754, 1-12 (2004).
[CrossRef]

F. Schellenberg, "Resolution enhancement technology: The past, the present, and extensions for the future," Proc. SPIE 5377, 1-20 (2004).
[CrossRef]

2000 (1)

P. Berman, A. Kahng, D. Vidhani, H. Wang, and A. Zelikovsky, "Optimal phase conflict removal for layout of dark field alternating phase shifting masks," IEEE Trans.Comput.-Aided Des. 19, 175-187 (2000).
[CrossRef]

1995 (3)

A. Moniwa and T. Terasawa, "Heuristic method for phase-conflict minimization in automatic phase-shift mask design," Jpn. J. Appl. Phys. 34, 6584-6589 (1995).
[CrossRef]

S. Sherif, B. Saleh, and R. Leone, "Binary image synthesis using mixed linear integer programming," IEEE Trans. Image Process. 4, 1252-1257 (1995).
[CrossRef] [PubMed]

N. Cobb and A. Zakhor, "Fast sparse aerial image calculation for OPC," Proc. SPIE 2621, 534-545 (1995).
[CrossRef]

1994 (1)

1992 (1)

Y. Liu and A. Zakhor, "Binary and phase-shifting image design for optical lithography," IEEE Trans. Semicond. Manuf. 5, 138-151 (1992).
[CrossRef]

1990 (1)

Y. Liu and A. Zakhor, "Optimal binary image design for optical lithography," Proc. SPIE 1264, 410-412 (1990).

1985 (1)

1981 (1)

B. Saleh and S. Sayegh, "Reductions of errors of microphotographic reproductions by optical corrections of original masks," Opt. Eng. 20, 781-784 (1981).

Abrams, D.

L. Pang, Y. Liu, and D. Abrams, "Inverse lithography technology (ILT): What is the impact to the photomask industry?" Proc. SPIE 6283, 62830X (2006).
[CrossRef]

Abrams, D. S.

D. S. Abrams and L. Pang, "Fast inverse lithography technology," Proc. SPIE 6154, 534-542 (2006).

Arce, G. R.

Berman, P.

P. Berman, A. Kahng, D. Vidhani, H. Wang, and A. Zelikovsky, "Optimal phase conflict removal for layout of dark field alternating phase shifting masks," IEEE Trans.Comput.-Aided Des. 19, 175-187 (2000).
[CrossRef]

Cobb, N.

N. Cobb and A. Zakhor, "Fast sparse aerial image calculation for OPC," Proc. SPIE 2621, 534-545 (1995).
[CrossRef]

Dai, G.

C. Hung, B. Zhang, E. Guo, L. Pang, Y. Liu, K. Wang, and G. Dai, "Pushing the lithography limit: Applying inverse lithography technology (ILT) at the 65nm generation," Proc. SPIE 6154, 61541M (2006).
[CrossRef]

Granik, Y.

Y. Granik, "Solving inverse problems of optimal microlithography," Proc. SPIE 5754, 506-526 (2004).
[CrossRef]

Guo, E.

C. Hung, B. Zhang, E. Guo, L. Pang, Y. Liu, K. Wang, and G. Dai, "Pushing the lithography limit: Applying inverse lithography technology (ILT) at the 65nm generation," Proc. SPIE 6154, 61541M (2006).
[CrossRef]

Hung, C.

C. Hung, B. Zhang, E. Guo, L. Pang, Y. Liu, K. Wang, and G. Dai, "Pushing the lithography limit: Applying inverse lithography technology (ILT) at the 65nm generation," Proc. SPIE 6154, 61541M (2006).
[CrossRef]

Kahng, A.

P. Berman, A. Kahng, D. Vidhani, H. Wang, and A. Zelikovsky, "Optimal phase conflict removal for layout of dark field alternating phase shifting masks," IEEE Trans.Comput.-Aided Des. 19, 175-187 (2000).
[CrossRef]

Kailath, T.

Leone, R.

S. Sherif, B. Saleh, and R. Leone, "Binary image synthesis using mixed linear integer programming," IEEE Trans. Image Process. 4, 1252-1257 (1995).
[CrossRef] [PubMed]

Liu, Y.

L. Pang, Y. Liu, and D. Abrams, "Inverse lithography technology (ILT): What is the impact to the photomask industry?" Proc. SPIE 6283, 62830X (2006).
[CrossRef]

C. Hung, B. Zhang, E. Guo, L. Pang, Y. Liu, K. Wang, and G. Dai, "Pushing the lithography limit: Applying inverse lithography technology (ILT) at the 65nm generation," Proc. SPIE 6154, 61541M (2006).
[CrossRef]

Y. Liu and A. Zakhor, "Binary and phase-shifting image design for optical lithography," IEEE Trans. Semicond. Manuf. 5, 138-151 (1992).
[CrossRef]

Y. Liu and A. Zakhor, "Optimal binary image design for optical lithography," Proc. SPIE 1264, 410-412 (1990).

Ma, X.

Mack, C. A.

C. A. Mack, "30 years of lithography simulation," Proc. SPIE 5754, 1-12 (2004).
[CrossRef]

Milanfar, P.

A. Poonawala and P. Milanfar, "Mask design for optical microlithography ???an inverse imaging problem," IEEE Trans. Image Process. 16, 774-788 (2007).
[CrossRef] [PubMed]

A. Poonawala and P. Milanfar, "OPC and PSM design using inverse lithography: A nonlinear optimization approach," Proc. SPIE 6154, 61543H (2006).
[CrossRef]

A. Poonawala and P. Milanfar, "Prewarping techniques in imaging: Applications in nanotechnology and biotechnology," Proc. SPIE 5674, 114-127 (2005).
[CrossRef]

Moniwa, A.

A. Moniwa and T. Terasawa, "Heuristic method for phase-conflict minimization in automatic phase-shift mask design," Jpn. J. Appl. Phys. 34, 6584-6589 (1995).
[CrossRef]

Nashold, K.

Pang, L.

L. Pang, Y. Liu, and D. Abrams, "Inverse lithography technology (ILT): What is the impact to the photomask industry?" Proc. SPIE 6283, 62830X (2006).
[CrossRef]

C. Hung, B. Zhang, E. Guo, L. Pang, Y. Liu, K. Wang, and G. Dai, "Pushing the lithography limit: Applying inverse lithography technology (ILT) at the 65nm generation," Proc. SPIE 6154, 61541M (2006).
[CrossRef]

D. S. Abrams and L. Pang, "Fast inverse lithography technology," Proc. SPIE 6154, 534-542 (2006).

Pati, Y. C.

Poonawala, A.

A. Poonawala and P. Milanfar, "Mask design for optical microlithography ???an inverse imaging problem," IEEE Trans. Image Process. 16, 774-788 (2007).
[CrossRef] [PubMed]

A. Poonawala and P. Milanfar, "OPC and PSM design using inverse lithography: A nonlinear optimization approach," Proc. SPIE 6154, 61543H (2006).
[CrossRef]

A. Poonawala and P. Milanfar, "Prewarping techniques in imaging: Applications in nanotechnology and biotechnology," Proc. SPIE 5674, 114-127 (2005).
[CrossRef]

Saleh, B.

S. Sherif, B. Saleh, and R. Leone, "Binary image synthesis using mixed linear integer programming," IEEE Trans. Image Process. 4, 1252-1257 (1995).
[CrossRef] [PubMed]

K. Nashold and B. Saleh, "Image construction through diffraction-limited high-contrast imaging systems: An iterative approach," J. Opt. Soc. Am. A 2, 635-643 (1985).
[CrossRef]

B. Saleh and S. Sayegh, "Reductions of errors of microphotographic reproductions by optical corrections of original masks," Opt. Eng. 20, 781-784 (1981).

Sayegh, S.

B. Saleh and S. Sayegh, "Reductions of errors of microphotographic reproductions by optical corrections of original masks," Opt. Eng. 20, 781-784 (1981).

Schellenberg, F.

F. Schellenberg, "Resolution enhancement technology: The past, the present, and extensions for the future," Proc. SPIE 5377, 1-20 (2004).
[CrossRef]

Sherif, S.

S. Sherif, B. Saleh, and R. Leone, "Binary image synthesis using mixed linear integer programming," IEEE Trans. Image Process. 4, 1252-1257 (1995).
[CrossRef] [PubMed]

Terasawa, T.

A. Moniwa and T. Terasawa, "Heuristic method for phase-conflict minimization in automatic phase-shift mask design," Jpn. J. Appl. Phys. 34, 6584-6589 (1995).
[CrossRef]

Vidhani, D.

P. Berman, A. Kahng, D. Vidhani, H. Wang, and A. Zelikovsky, "Optimal phase conflict removal for layout of dark field alternating phase shifting masks," IEEE Trans.Comput.-Aided Des. 19, 175-187 (2000).
[CrossRef]

Wang, H.

P. Berman, A. Kahng, D. Vidhani, H. Wang, and A. Zelikovsky, "Optimal phase conflict removal for layout of dark field alternating phase shifting masks," IEEE Trans.Comput.-Aided Des. 19, 175-187 (2000).
[CrossRef]

Wang, K.

C. Hung, B. Zhang, E. Guo, L. Pang, Y. Liu, K. Wang, and G. Dai, "Pushing the lithography limit: Applying inverse lithography technology (ILT) at the 65nm generation," Proc. SPIE 6154, 61541M (2006).
[CrossRef]

Zakhor, A.

N. Cobb and A. Zakhor, "Fast sparse aerial image calculation for OPC," Proc. SPIE 2621, 534-545 (1995).
[CrossRef]

Y. Liu and A. Zakhor, "Binary and phase-shifting image design for optical lithography," IEEE Trans. Semicond. Manuf. 5, 138-151 (1992).
[CrossRef]

Y. Liu and A. Zakhor, "Optimal binary image design for optical lithography," Proc. SPIE 1264, 410-412 (1990).

Zelikovsky, A.

P. Berman, A. Kahng, D. Vidhani, H. Wang, and A. Zelikovsky, "Optimal phase conflict removal for layout of dark field alternating phase shifting masks," IEEE Trans.Comput.-Aided Des. 19, 175-187 (2000).
[CrossRef]

Zhang, B.

C. Hung, B. Zhang, E. Guo, L. Pang, Y. Liu, K. Wang, and G. Dai, "Pushing the lithography limit: Applying inverse lithography technology (ILT) at the 65nm generation," Proc. SPIE 6154, 61541M (2006).
[CrossRef]

IEEE Trans. (1)

P. Berman, A. Kahng, D. Vidhani, H. Wang, and A. Zelikovsky, "Optimal phase conflict removal for layout of dark field alternating phase shifting masks," IEEE Trans.Comput.-Aided Des. 19, 175-187 (2000).
[CrossRef]

IEEE Trans. Image Process. (2)

A. Poonawala and P. Milanfar, "Mask design for optical microlithography ???an inverse imaging problem," IEEE Trans. Image Process. 16, 774-788 (2007).
[CrossRef] [PubMed]

S. Sherif, B. Saleh, and R. Leone, "Binary image synthesis using mixed linear integer programming," IEEE Trans. Image Process. 4, 1252-1257 (1995).
[CrossRef] [PubMed]

IEEE Trans. Semicond. Manuf. (1)

Y. Liu and A. Zakhor, "Binary and phase-shifting image design for optical lithography," IEEE Trans. Semicond. Manuf. 5, 138-151 (1992).
[CrossRef]

J. Opt. Soc. Am. A (2)

Jpn. J. Appl. Phys. (1)

A. Moniwa and T. Terasawa, "Heuristic method for phase-conflict minimization in automatic phase-shift mask design," Jpn. J. Appl. Phys. 34, 6584-6589 (1995).
[CrossRef]

Opt. Eng. (1)

B. Saleh and S. Sayegh, "Reductions of errors of microphotographic reproductions by optical corrections of original masks," Opt. Eng. 20, 781-784 (1981).

Opt. Express (1)

Proc. SPIE (10)

Y. Granik, "Solving inverse problems of optimal microlithography," Proc. SPIE 5754, 506-526 (2004).
[CrossRef]

D. S. Abrams and L. Pang, "Fast inverse lithography technology," Proc. SPIE 6154, 534-542 (2006).

C. Hung, B. Zhang, E. Guo, L. Pang, Y. Liu, K. Wang, and G. Dai, "Pushing the lithography limit: Applying inverse lithography technology (ILT) at the 65nm generation," Proc. SPIE 6154, 61541M (2006).
[CrossRef]

L. Pang, Y. Liu, and D. Abrams, "Inverse lithography technology (ILT): What is the impact to the photomask industry?" Proc. SPIE 6283, 62830X (2006).
[CrossRef]

A. Poonawala and P. Milanfar, "Prewarping techniques in imaging: Applications in nanotechnology and biotechnology," Proc. SPIE 5674, 114-127 (2005).
[CrossRef]

A. Poonawala and P. Milanfar, "OPC and PSM design using inverse lithography: A nonlinear optimization approach," Proc. SPIE 6154, 61543H (2006).
[CrossRef]

C. A. Mack, "30 years of lithography simulation," Proc. SPIE 5754, 1-12 (2004).
[CrossRef]

F. Schellenberg, "Resolution enhancement technology: The past, the present, and extensions for the future," Proc. SPIE 5377, 1-20 (2004).
[CrossRef]

Y. Liu and A. Zakhor, "Optimal binary image design for optical lithography," Proc. SPIE 1264, 410-412 (1990).

N. Cobb and A. Zakhor, "Fast sparse aerial image calculation for OPC," Proc. SPIE 2621, 534-545 (1995).
[CrossRef]

Other (11)

A. K.-K. Wong, Resolution enhancement techniques in optical lithography (SPIE Press, Bellingham, Washington, 2001).
[CrossRef]

S. H. Chan, A. K. Wong, and E. Y. Lam, "Inverse synthesis of phase-shifting mask for optical lithography," in "OSA Topical Meeting in Signal Recovery and Synthesis," (2007), p. SMD3.

J. Plummer, M. Deal, and P. Griffin, Silicon VLSI Technology ??? Fundamentals, Practice and Modeling (Prentice Hall, 2000).

J. W. Goodman, Statistical Optics (Wiley-Interscience, 1985).

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company Publisher, Englewood, Colo, 2005), 3rd ed.

L. G. Shapiro and G. C. Stockman, Computer Vision (Prentice Hall, 2001).

D. Halliday, R. Resnick, and K. S. Krane, Physics, (John Wiley and Sons, New York, 2002), 2nd ed., Vol. 2.

S. H. Chan and E. Y. Lam, "Inverse image problem of designing phase shifting masks in optical lithography," in "IEEE International Conference on Image Processing," (2008).

P. E. Gill, W. Murray, and M. H. Wright, Practical optimization (Academic Press, London, 1986).

W. Rudin, Principles of Mathematical Analysis (McGraw-Hill, 1976).

M. Minoux, Mathematical programming theory and algorithms (John Wiley and Sons, Chichester, 1986).

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Figures (11)

Fig. 1.
Fig. 1.

A simplified diagram of an optical projection lithography system. There are two processes: projection optics, and photoresist development, and four basic elements: source, mask, lens, and wafer.

Fig. 2.
Fig. 2.

Development of an infinite-contrast resist can be defined by the threshold.

Fig. 3.
Fig. 3.

Principle of phase shifting masks and the difficulty of phase assignment.

Fig. 4.
Fig. 4.

Definitions and approximations to define various distance functions

Fig. 5.
Fig. 5.

Example pattern for conversion of a mask pattern into a graph.

Fig. 6.
Fig. 6.

Illustration of DP computation. Numbers represent the accumulated costs to reach the node. Circled nodes are nodes with lowest accumulated cost at their stages.

Fig. 7.
Fig. 7.

Flow chart of the phase initialization algorithm, where function f denotes the accumulated cost.

Fig. 8.
Fig. 8.

Results of phase initialization. We used Eq. (11) as the distance function.

Fig. 9.
Fig. 9.

Inverse imaging applied to an XOR gate pattern.

Fig. 10.
Fig. 10.

Four-bar example.

Fig. 11.
Fig. 11.

Two-rectangle example.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

H ( x , y ) = H ˜ ( f , g ) exp { j 2 π ( fx + gy ) } d f d g = J 1 ( 2 π r NA λ ) 2 π r NA λ ,
I aerial ( x , y ) = E ( x , y ) 2 = H ( x , y ) * O ( x , y ) 2 .
I ( x , y ) = sig { I aerial ( x , y ) } = 1 1 + exp { a ( I aerial ( x , y ) t r ) } ,
F = Σ x , y ( I ( x , y ) I ̂ ( x , y ) ) 2 = Σ x , y [ 1 1 + e a ( H ( x , y ) * O ( x , y ) 2 t r ) I ̂ ( x , y ) ] 2 .
O opt ( x , y ) = arg min F . O ( x , y ) { 1 , 0 , 1 }
F = 4 a { H ( x , y ) * [ ( I ̂ ( x , y ) I ( x , y ) ) · I ( x , y ) · ( 1 I ( x , y ) ) · ( H ( x , y ) * O ( x , y ) ) ] } ,
R = 18 O ( x , y ) 3 + 2 O ( x , y ) .
d 1 ( i , j ) = Σ k G k W k ,
d 2 ( i , j ) = ( Σ k W k G k 2 ) 1 .
E = 1 4 π ε 0 2 λ y l 2 y 2 + ( l 2 ) 2 .
d 3 ( i , j ) = ( Σ k W k 2 G k G k 2 + ( W k 2 ) 2 ) 1 .
V = I max I min I max + I min × 100 % .
NILS = CD I threshold d I dx I threshold ,

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